A bandgap voltage reference circuit can be used, e.g., to provide a substantially constant reference voltage for a circuit that operates in an environment where the temperature fluctuates. A bandgap voltage reference circuit typically adds a voltage complimentary to absolute temperature (VCTAT) to a voltage proportional to absolute temperature (VPTAT) to produce a bandgap reference output voltage (VGO). The VCTAT is typically a simple diode voltage, also referred to as a base-to-emitter voltage drop, forward voltage drop, base-emitter voltage, or simply VBE. Such a diode voltage is typically provided by a diode connected transistor (i.e., a BJT transistor having its base and collector connected together). The VPTAT can be derived from one or more VBE, where ΔVBE (delta VBE) is the difference between the VBEs of BJT transistors having different emitter areas and/or currents, and thus, operating at different current densities.
FIG. 1A illustrates an exemplary conventional bandgap voltage reference circuit 100, including transistors Q1 through QN connected in parallel (in the “N” branch), a transistor QN+1 (in the “1” branch), and a further transistor QN+2 (in the “CTAT” branch).
The bandgap voltage reference circuit 100 also includes an amplifier 120 and three PMOS transistors M1, M2 and M3 that are configured to function as current sources that supply currents to the “N”, “1”, and “CTAT” branches. Since the gates of the PMOS transistors are tied together, and their source terminals are all connected to the positive voltage rail (VDD), the source-to-gate voltages of these transistors are equal. As a result, the “N”, “1”, and “CTAT” branches receive and operate at approximately the same current, Iptat.
In FIG. 1A the transistor QN+2 is used to generate the VCTAT, and the transistors Q1 through QN in conjunction with transistor QN+1 are used to generate the VPTAT. More specifically, the VCTAT is a function of the base emitter voltage (VBE) of diode connected transistor QN+2, and the VPTAT is a function of ΔVBE, which is a function of the difference between the base-emitter voltage of transistor QN+1 and the base-emitter voltage of diode connected transistors Q1 through QN connected in parallel.
Due to negative feedback, the amplifier 120 adjusts the common PMOS gate voltage of current source transistors M1, M2 and M3 until the non-inverting (+) and inverting (−) inputs of the amplifier 120 are at equal voltage potentials. This occurs when Iptat*R1+VBE1, 2 . . . , n=VBEn+1, where VBE1, 2, . . . , n=VBEn+1−ΔVBE. Thus, Iptat=ΔVBE/R1.
Here, the bandgap voltage output (VGO) is as follows:
                                          V            ⁢                                                  ⁢            G            ⁢                                                  ⁢            O                    =                    ⁢                                    V              ⁢                                                          ⁢              C              ⁢                                                          ⁢              T              ⁢                                                          ⁢              A              ⁢                                                          ⁢              T                        +                          V              ⁢                                                          ⁢              P              ⁢                                                          ⁢              T              ⁢                                                          ⁢              A              ⁢                                                          ⁢              T                                      ,                                =                ⁢                              V            ⁢                                                  ⁢            B            ⁢                                                  ⁢            E                    +                      R            ⁢                                                  ⁢                          2              /              R                        ⁢                                                  ⁢            1            *                          V              T                        *                                          ln                ⁡                                  (                  N                  )                                            .                                          
where Vt is the thermal voltage, which is about 26 mV at room temperature.
If VBE˜0.7V, and R2/R1*VT*ln(N)˜0.5V, then VGO˜1.2V.
The current sources can be implemented using alternative configurations than shown in FIG. 1A. Accordingly, FIG. 1B is provided to show the more general circuit. As was the case in FIG. 1A, in FIG. 1B the amplifier 120 controls the current sources I1, I2 and I3.
The voltage across R2 is proportioned to temperature and when it is scaled to about 0.5V at room temperature it makes VGO relatively constant with temperature by compensating the negative temperature coefficient of VBE3 (i.e., the base emitter voltage of transistor Q3).
For N=8, which is a common value for N,
            R      ⁢                          ⁢      2              R      ⁢                          ⁢      1        ~  9for a good temperature coefficient (tempco) of VGO. R2 can be provided by connecting three unit resistors in series, and R1 can be provided by connecting another three unit resistors in parallel. This is a common practice and makes the ratio of 9 very accurate in manufactured circuits.
In practice, long term drift in unit resistor values can cause long term drift in VGO, which is undesirable.